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Unification in sort theories and its applications

Christoph Weidenbach
<span title="">1996</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j2td7x4trvgx7pjoienrccryxq" style="color: black;">Annals of Mathematics and Artificial Intelligence</a> </i> &nbsp;
In this language sorted unification in elementary sort theories is of unification type finitary.  ...  The notions of a sort and a sort theory are developed in a way such that a standard calculus can be turned into a sorted calculus by replacing standard unification with sorted unification.  ...  As a result of the extended sort language it is shown that unification in elementary sort theories is decidable and of unification type finitary.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf02127750">doi:10.1007/bf02127750</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gdyscp3ddvepnokebhmwtqs434">fatcat:gdyscp3ddvepnokebhmwtqs434</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170815213644/http://pubman.mpdl.mpg.de/pubman/item/escidoc:1834298/component/escidoc:1857779/MPI-I-93-211.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7e/e6/7ee6ba33a3cee9442d07a70bc67465b4a5fb5952.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf02127750"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Unification and Narrowing in Maude 2.4 [chapter]

Manuel Clavel, Francisco Durán, Steven Eker, Santiago Escobar, Patrick Lincoln, Narciso Martí-Oliet, José Meseguer, Carolyn Talcott
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Unification is supported in Core Maude, the core rewriting engine of Maude, with commands and metalevel functions for order-sorted unification modulo some frequently occurring equational axioms.  ...  These features include communication with external objects, a new implementation of its module algebra, and new predefined libraries. We also review some new Maude applications.  ...  unification problem, it is important to restrict ourselves to order-sorted equational theories.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-02348-4_27">doi:10.1007/978-3-642-02348-4_27</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/adxberqkxrhnviqr4ce2aflcfy">fatcat:adxberqkxrhnviqr4ce2aflcfy</a> </span>
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User-Defined Nonmonotonicity in Unification-Based Formalisms [article]

Lena Stromback (Department of Computer and Information Science Linkoping University, Sweden)
<span title="1995-05-17">1995</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we show how nonmonotonic operations can also be user-defined by applying default logic (Reiter 1980) and generalizing previous results on nonmonotonic sorts (Young & Rounds 1993).  ...  A common feature of recent unification-based grammar formalisms is that they give the user the ability to define his own structures.  ...  I would also like to thank Lars Ahrenberg and Patrick Doherty for comments on this work and Mark A. Young for providing me with much-needed information about his and Bill Rounds' work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cmp-lg/9505033v2">arXiv:cmp-lg/9505033v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oxrde5mknnhc3nbbdyv3sgqwiu">fatcat:oxrde5mknnhc3nbbdyv3sgqwiu</a> </span>
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User-defined nonmonotonicity in unification-based formalisms

Lena Strömbäck
<span title="">1995</span> <i title="Association for Computational Linguistics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5n6volmnonf5tn6xputi5f2t3e" style="color: black;">Proceedings of the 33rd annual meeting on Association for Computational Linguistics -</a> </i> &nbsp;
In this paper we show how nonmonotonic operations can also be user-defined by applying default logic (Reiter, 1980) and generalizing previous results on nonmonotonic sorts (Young and Rounds, 1993) .  ...  However, this possibility is mostly limited and does not include nonmonotonic operations.  ...  I would also like to thank Lars Ahrenberg and Patrick Doherty for comments on this work and Mark A. Young for providing me with much-needed information about his and Bill Rounds' work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3115/981658.981667">doi:10.3115/981658.981667</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/acl/Stromback95.html">dblp:conf/acl/Stromback95</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o4rnyrbdhbhlzgjjelqs36yshy">fatcat:o4rnyrbdhbhlzgjjelqs36yshy</a> </span>
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Variants, Unification, Narrowing, and Symbolic Reachability in Maude 2.6

Francisco Duran, Steven Eker, Santiago Escobar, Jose Meseguer, Carolyn Talcott, Marc Herbstritt
<span title="2011-04-26">2011</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wkjtc7dggzfktmoov66odshrra" style="color: black;">International Conference on Rewriting Techniques and Applications</a> </i> &nbsp;
We have added support in Maude 2.6 for: (i) order-sorted unification modulo associativity, commutativity and identity, (ii) variant generation, (iii) order-sorted unification modulo finite variant theories  ...  We also explain how these features have a number of interesting applications in areas such as unification theory, cryptographic protocol verification, business processes, and proofs of termination, confluence  ...  We are very thankful to the other members of the Maude team, namely, Manuel Clavel, Patrick Lincoln, and Narciso Martí-Oliet, with whom we have designed and built the Maude language and system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.rta.2011.31">doi:10.4230/lipics.rta.2011.31</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/rta/DuranEEMT11.html">dblp:conf/rta/DuranEEMT11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zqh55brfcna45bt43enmxm3rli">fatcat:zqh55brfcna45bt43enmxm3rli</a> </span>
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An order-sorted resolution in theory and practice

Trudy Weibel
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
The proposed order-sorted system passes the final feasibility check with its successful implementation and actual use in the verification application. *  ...  Our techniques use Frisch's hybrid model, which localises the sort information in the sort reasoner, and Walther's sorted unification algorithm.  ...  Acknowledgements I would like to thank the anonymous referees and the editor for many helpful suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(97)00051-0">doi:10.1016/s0304-3975(97)00051-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tzaakwa7h5e25is7qcohmpjc4y">fatcat:tzaakwa7h5e25is7qcohmpjc4y</a> </span>
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A logical semantics for nonmonotonic sorts

Mark A. Young, Bill Rounds
<span title="">1993</span> <i title="Association for Computational Linguistics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5n6volmnonf5tn6xputi5f2t3e" style="color: black;">Proceedings of the 31st annual meeting on Association for Computational Linguistics -</a> </i> &nbsp;
In particular, we show how nonmonotonic sort unification is equivalent to finding the smallest default theory that describes both NSFSs; and also how taking a solution for a NSFS is the same as finding  ...  Suppose we have a feature system, and we wish to add default values in a well-defined way. We might start with Kasper-Rounds logic, and use Reiter's example to form it into a default logic.  ...  The suffix +re is applicable and so appears in the extension. DKRL AND NONMONOTONIC SORTS In the previous section we defined how to get the right answers from a system using default sorts.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3115/981574.981602">doi:10.3115/981574.981602</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/acl/YoungR93.html">dblp:conf/acl/YoungR93</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/julhmo4mvjb6rilhn3dx4tkhlu">fatcat:julhmo4mvjb6rilhn3dx4tkhlu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110402015238/http://aclweb.org/anthology-new/P/P93/P93-1028.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f3/53/f353dc205d5585f110427aa9fd9f76ee2a370f08.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3115/981574.981602"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 1117 of Mathematical Reviews Vol. , Issue 96b [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A spe- cial chapter is devoted to higher-order unification, unification in sort theories and constraint solving.  ...  The main emphasis is given to first-order (theory) unification, but the paper also contains substantial information on higher-order unification and unification in sort theories.  ... 
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Special issue on automated deduction: Decidability, complexity, tractability

Silvio Ghilardi, Viorica Sofronie-Stokkermans, Ulrike Sattler, Ashish Tiwari
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ezljl2d3lzga5efenbxdvvfcpa" style="color: black;">Journal of symbolic computation</a> </i> &nbsp;
Although general logical formalisms (predicate logic, set theory, number theory) are undecidable or not even recursively enumerable, it is often the case that in applications only special fragments need  ...  The main result in this paper is a characterization of a decidable fragment of many-sorted first-order logics important in applications.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jsc.2009.05.006">doi:10.1016/j.jsc.2009.05.006</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ojjvruw2jza6tpamkmmgyfk3cq">fatcat:ojjvruw2jza6tpamkmmgyfk3cq</a> </span>
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Order-sorted Equational Unification Revisited

Joe Hendrix, José Meseguer
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
In many examples of interest, using order-sorted unification over unsorted unification is able to reduce the total number of unifiers considered, and dramatically improve the performance of the Maude-NRL  ...  We have implemented this algorithm in Maude for use with the Maude-NRL protocol analyzer and have used CiME for unsorted E-unification for E any set of AC and ACU axioms.  ...  In Section 4, we illustrate how it can be used for AC and ACU order-sorted unification in Maude and, in Section 5 we prove its correctness.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2012.11.010">doi:10.1016/j.entcs.2012.11.010</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uqqx5qefcbccvnbq2i62lwzptm">fatcat:uqqx5qefcbccvnbq2i62lwzptm</a> </span>
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Page 8134 of Mathematical Reviews Vol. , Issue 2000k [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Via the relativization of sort theories and tree automata to monadic Horn clauses it is possible to compare these approaches.  ...  In the third section, we mention some unification results for specific equational theories.  ... 
<span class="external-identifiers"> </span>
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Page 4109 of Mathematical Reviews Vol. , Issue 94g [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In this paper we develop a sorted version of type theory; we ex- tend the syntax and semantics of simple type theory by a higher order sort concept that includes term declarations.  ...  We present a differ- ence matching algorithm, its properties, several applications, and suggest extensions.”  ... 
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Theories of Homomorphic Encryption, Unification, and the Finite Variant Property

Fan Yang, Santiago Escobar, Catherine Meadows, José Meseguer, Paliath Narendran
<span title="">2014</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mht6wa2vdbg7dn6n6lws4hpzti" style="color: black;">Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming - PPDP &#39;14</a> </i> &nbsp;
Recent advances in the automated analysis of cryptographic protocols have aroused new interest in the practical application of unification modulo theories, especially theories that describe the algebraic  ...  However, this application requires unification algorithms that can be easily implemented and easily extended to combinations of different theories of interest.  ...  Assuming that the distributive equation is oriented as the rewrite rule e(X * Y ) → e(X) * e(Y ), Related Work in Equational Unification and its Application to Decompositions of AGH Equational theories  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2643135.2643154">doi:10.1145/2643135.2643154</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ppdp/YangEMMN14.html">dblp:conf/ppdp/YangEMMN14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ss5awwz6wffnnlp6i67rg5svcu">fatcat:ss5awwz6wffnnlp6i67rg5svcu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829112612/http://publish.illinois.edu/science-of-security-lablet/files/2014/06/Theories-of-Homomorphic-Encryption-Unification-and-the-Finite-Variant-Property.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1e/13/1e13976be29f40532db936c37892cea90e3e78ae.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2643135.2643154"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Unification theory

Jörg H. Siekmann
<span title="">1989</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ezljl2d3lzga5efenbxdvvfcpa" style="color: black;">Journal of symbolic computation</a> </i> &nbsp;
This article surveys what is presently known in unification theory and records its early history. 20g  ...  This operation, called unification in work on deduction, is the "addition-and-multiplication" of AI-systems and is consequently often supported by special purpose hardware or by a fast instruction set  ...  applications in physics in more modem times), unification theory derives its impetus from its numerous applications in AI and computer science.  ... 
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Page 2967 of Mathematical Reviews Vol. , Issue 99e [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In or- der to prove decidability of unification in the extensions, a class of Horn clause sets called sorted shallow equational theories is in- troduced.  ...  So-called semi-linear equational theories can be effectively transformed into equivalent sorted shallow equational theories and generalize the classes of shallow and standard equational theories.”  ... 
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